Collaborative Efforts: How A and B Can Complete a Job Together

Introduction to Collaborative Work Problems

Efficiency and collaboration are key components in achieving tasks within a specified time frame. This article delves into the problem of two workers, A and B, working together to complete a job. We will explore the methods to determine the time required for them to finish the job by using their individual work rates and the combined work rate. Understanding this concept is crucial for project managers and team leaders aiming to optimize resource utilization and improve productivity.

Understanding Individual Work Rates

In scenarios involving collaborative work, it is essential to first understand the individual work rates of the participants. In this context, let's consider a situation where individual worker A can complete a job in 8 hours, and individual worker B can complete the same job in 12 hours. We will calculate their individual work rates and then determine how long it will take for A and B to complete the job together.

Individual Work Rates of A and B

Calculating the individual work rates for A and B:

Worker A: A can complete the job in 8 hours, so A's work rate is 1/8 of the job per hour. Worker B: B can complete the job in 12 hours, so B's work rate is 1/12 of the job per hour.

Combined Work Rate

By combining their work rates, we can determine how much of the job they can complete together in one hour. To do this, we add their individual work rates:

Combined work rate 1/8 1/12

Before adding these fractions, we need a common denominator. The least common multiple of 8 and 12 is 24:

1/8 3/24 1/12 2/24

Adding these fractions, we get:

3/24 2/24 5/24

Hence, the combined work rate is 5/24 of the job per hour.

Time Required to Complete the Job Together

Now, to find out the time required for A and B to complete the job together, we take the reciprocal of their combined work rate:

Time to complete the job 1 / (5/24) 24/5 hours

Calculating 24/5:

24/5 4.8 hours

This means that A and B can complete the job together in 4.8 hours, or more specifically, 4 hours and 48 minutes.

Conclusion

Collaborative work problems, such as the one involving A and B, are common in various fields, from project management to everyday tasks. Understanding the principles of work rates and combined work rates can help optimize resource allocation and enhance team productivity. By applying these concepts, you can efficiently determine how long it takes for multiple individuals to complete a task together, ensuring that projects are completed on time and within budget.